Image quality depends 90% on the mother lens, rather than the telecon - all they do is enlarge what's already there. Which is why 1.4x is always better than 1.7x or 2x.
I tested nine telecons side by side with three 70-200/2.8s (flippin thousands of images) and the main findings were there's very little difference in sharpness between different brands of the same magnification on the same lens, and no noticeable difference in AF speed either. Only IQ difference worth noting was edge sharpness, comparing say Canon Mk3 with Kenko, but even that's not massive, and given the kind of subjects you're likely to shoot at 300-400mm, edges will quite probably be out of focus anyway.
If it makes a difference, Kenkos have a plastic barrel, Canon, Nikon and Sigma telecons are metal. The other point worth making is it's possible some telecon/lens combos will work better than others with certain lens designs, depending on how the image is presented to the telecom from the rear of the lens, but as a general rule, the longer the better.